If a taxpayer owes arrearages of taxes due to an administrative error, the county may not bill, collect, claim a lien for, or sell the arrearages of taxes for tax years earlier than the 2 most recent tax years, including the current tax year. If a taxpayer owes arrearages of taxes due to an administrative error, the county collector shall send the taxpayer, by certified mail, a notice that the arrearages of taxes are owed by the taxpayer. If the notice is mailed to the taxpayer on or before October 1 in any year, then (i) the county collector may send a separate bill for the arrearages of taxes, which may be due no sooner than 30 days after the due date for the next installment of taxes or (ii) the arrearages of taxes may be added to the tax bill for the following year, in which case the taxes are due in 2 equal installments on June 1 and September 1 in the following year unless the county has adopted an accelerated method of billing in which case the arrearages of taxes may be billed separately and shall be due in equal installments on the dates on which each installment of taxes is due in the following year. If the notice is mailed after October 1 in any year, then the arrearages of taxes are to be added to the tax bill for the second year after the notice and are due in 2 equal installments on June 1 and September 1 in the second year after the notice unless the county has adopted an accelerated method of billing in which case the arrearages of taxes may be billed separately and shall be due in equal installments on the dates on which each installment of taxes is due in the second year after the notice. In no event shall the due dates on the arrearages of taxes be in more than one tax year. The arrearages of taxes added to a tax bill under this Section are to be listed separately on the tax bill. “Administrative error” includes but is not limited to failure to include an extension for a taxing district on the tax bill, an error in the calculations of tax rates or extensions or any other mathematical error by the county clerk, or a defective coding by the county, but does not include a failure by the county to send a tax bill to the taxpayer, the failure by the taxpayer to notify the assessor of a change in the tax-exempt status of property, or any error concerning the assessment of the property.